臺灣博碩士論文加值系統

摘要
運算轉導放大器(OTA)是目前類比電路設計公認最佳的主動元件。而本論文所使用的運算轉阻放大器(OTRA)，因其與OTA有對偶的關係，且其輸入端為虛接地，所以沒有寄生效應，使它在設計電路上有著先天的優勢。
過去以OTRA為主動元件的電路設計，學者們都假設Rm(s)為無限大，而使電路有相當大的誤差。而本論文則是假設Rm(s)為有限值，便可令Rm(s)近似為轉移等效電容 ，以此設計二階無電容振盪器。
在電路設計的部分，其基本架構為OTRA的正負輸入端和輸入電壓間連接電阻，且有以下四種特性，1.每個方程式需包含一個由OTRA實現的轉移等效電容2.方程式中除轉移電容為正的一項外，將其他各項移往方程式的另一邊，正項表示信號從OTRA的正端輸入3.方程式中除轉移電容為正的一項外，將其他各項移往方程式的另一邊，負項表示信號從OTRA的負端輸入，4.方程式不包含(Vi-Vj)G，再根據導納矩陣分析設計法，將轉移函式以矩陣的方式表示，分解成兩個方程式以基本電路架構而成，最後連結成整體電路。本論文電路驗證使用H-SPICE軟體中TSMC035 製程參數進行模擬，之後藉由振盪頻率公式對元件值做調整，使結果符合設計，並進一步以降低輸入的Vbias值和增加電路內部的閘極長度L的方式來改變振盪電路的振幅。

Abstract
Operational Trans-conductance Amplifier (OTA) is recognized as the best active components in the analog circuit design. We use OTRA for the active circuit components to design the circuit, because there are natural advantages in the design of circuit that is the input terminals of OTRA are internally grounded, thereby eliminating response limitations due to parasitic capacitances and resistances at the input. There are natural advantages in the design of circuit.
In the past, the transfer resistance of the OTRA is infinite cause the circuit more inaccuracy. But in this thesis we assume the value of the transfer resistance is limited, the Rm(s)=Rmo/1+(s/wo) , and let 1/wo*Rmo approximate equivalent transfer Capacitor to design the Second-Order Oscillator.
In the structure of circuit design for the resistances connect OTRA positive and negative input and input voltage, which has four features, 1. The positive variable on the right equation there must be a transfer equivalent capacitance. 2. The positive variable on the left equation equals the product of the OTRA positive terminal input voltage and conductance. 3. The negative variable on the left equation equals the product of the OTRA negative terminal input voltage and conductance. 4. Equation does not contain (Vi-Vj) G. Then according to admittance matrix analytical synthesis, we make the transfer function into a matrix and decomposed into two equations. The next step is establishing the basic circuit structure by these two equations and to form the whole circuit. This circuit was simulated by H-SPICE, and then we changed the value of components by formula of oscillator frequency to let our result conforms to our design. On the other hand, we modulated circuit’s amplitude by decrease the input‘s value of Vbias and increase L of OTRA.

目錄

摘要 I
Abstract II
誌謝 III
目錄 IV
圖目錄 V
表目錄 VII
第一章 緒 論 1
第二章 主動元件之介紹 3
2-1 相關主動元件的介紹 3
2-1.1運算放大器（Operational Amplifier） 4
2-1.2第一代電流傳輸器(CCI) 6
2-1.3第二代電流傳輸器(CCII) 8
2-1.4第三代電流傳輸器(CCIII) 11
2-1.5第二代電流控制傳輸器 (CCCII) 12
2-1.6差分差動電流傳輸器(Differential Difference Current Conveyor) 15
2-1.7第二代完全差動電流傳輸器(Fully Differential second-generation Difference Current Conveyor) 18
2-1.8運算轉導放大器（Operational Transconductance Amplifier） 20
2-2 運算轉阻放大器(OTRA)介紹 22
2-3 結論 32
第三章 以OTRA為主動元件發表之電路 33
3-1 以OTRA為主動元件發表之振盪電路 33
3-2 以OTRA為主動元件發表之其他功能電路 35
3-3 結論 40
第四章 以OTRA為主動元件設計二階振盪電路 41
4-1 振盪電路的介紹 41
4-2 電路設計 42
4-3 電路模擬 51
4-3.1電路模擬過程與結果 51
4-3.2 Vo1與Vo2的輸出相位差 54
4-4 電路近似與非近似誤差分析 55
4-5輸入端虛短路誤差分析 57
4-6振盪電路的振幅調整 59
4-7 結論 68
第五章 總結與未來研究方向 70
5-1 總結 70
5-2 未來研究方向 73
參 考 文 獻 74

圖目錄
圖2-1 理想放大器的Nullor 模型及電路符號 4
圖2-2 運算放大器電路架構方塊圖 5
圖2-3 運算放大器(OA)之內部電路 6
圖2-4 CCI 之元件符號 7
圖2-5 CCI 之Nullor 等效模型 7
圖2-6 CCII 之元件符號 8
圖2-7(a) CCII 之Nullor 模型 8
圖2-7(b) CCII 之簡化Nullor 模型 9
圖2-8(a) CCII+內部電路 10
圖2-8(b) CCII–內部電路 10
圖2-9 CCIII 之元件符號 11
圖2-10 以雙輸出端CCII 實現CCIII 12
圖2-11 CCIII 之CMOS 內部電路 12
圖2-12 CCCII正型之元件符號以及等效Nullor model 13
圖2-13 BJT型式實現之CCCII+ 14
圖2-14 以MOS實現之CCCII+之內部電路圖 15
圖2-15 正型DDCC之元件符號 16
圖2-16 負型DDCC之元件符號 16
圖2-17 正型DDCC之內部電路 16
圖2-18 負型DDCC之內部電路 17
圖2-19 利用電流鏡之技術來取代內部偏壓電流 17
圖2-20 FDCCII之元件符號 19
圖2-21 FDCCII之內部電路 19
圖2-22 利用電流鏡之技術製造反相電流輸出端 20
圖2-23 運算轉導放大器(OTA)之元件符號圖 21
圖2-24 運算轉導放大器(OTA)之Nullor等效模型 21
圖2-25 運算轉導放大器(OTA)之內部電路 22
圖2-26 OTRA之元件符號 23
圖2-27 由J.-J. Chen等學者提出之OTRA之內部電路 24
圖2-28 本論文之OTRA內部電路(2006年提出) 25
圖2-29 本論文使用之OTRA內部電路 26
圖2-30 OTRA的寄生效應關係圖 29
圖2-31 OTRA與後面所接電路關係圖 29
圖2-32 OTRA在開迴路（open loop）量測電路圖 30
圖2-33 OTRA直流轉阻增益值與偏壓變化關係 31
圖2-34 OTRA轉阻值的-3db頻率與偏壓變化關係 31
圖2-35 OTRA轉移等效電容與偏壓變化關係 32
圖3-1 K. N. Salama等學者所提出之雙OTRA構成的震盪器 33
圖3-2 Chun-Li Hou等學者所提出之OTRA構成的震盪器 34
圖3-3 Yu-Kang Lo等學者所提出之OTRA構成的單穩態多諧震盪器 35
圖3-4 Ugur Cam等學者所提出之一階全通濾波電路 36
圖3-5 Selquk Kiling等學者提出之一階全通濾波電路 37
圖3-6 Cem Cakir等學者提出之一階、二階全通濾波電路 38
圖3-7 Selcuk Kilinc等學者所提出之二階多功濾波電路 39
圖4-1 回授系統 41
圖4-2 迴路分析法示意圖 43
圖4-3 迴路分析法示意圖-2 43
圖4-4 節點分析法示意圖 44
圖4-5 節點分析法示意圖-2 44
圖4-6 使用OTRA設計電路架構圖 45
圖4-7 設計本論文之二階振盪電路(1) 49
圖4-8 設計本論文之二階振盪電路(2) 50
圖4-9 設計本論文之二階振盪電路(3) 50
圖4-10 設計本論文之二階振盪電路(4) 50
圖4-11 表4-1元件值的模擬結果 52
圖4-12 R2R3為140k的模擬結果 53
圖4-13 R2R3為130k的模擬結果 53
圖4-14 Vo1與Vo2輸出圖形 54
圖4-15 寄生電容、寄生電導表示圖 57
圖4-16 L不變、Vbias=-0.6時的輸出波型圖 59
圖4-17 L不變、Vbias=-0.6時的頻譜圖 60
圖4-18 倍時的波型圖 61
圖4-19 倍時的頻譜圖 61
圖4-20 倍時的波型圖 62
圖4-21 倍時的頻譜圖 62
圖4-22 倍時的波型圖 63
圖4-23 倍時的頻譜圖 63
圖4-24 倍時的波型圖 64
圖4-25 倍時的頻譜圖 64
圖4-26 THD-Vbias1圖 66
圖4-27 THD-Vbias2圖 66
圖4-28 amplitude-Vbias1圖 67
圖4-29 amplitude-Vbias2圖 67
圖4-30 THD-amplitude圖 68

表目錄
表2-1 工作電壓及電流的範圍 9
表2-2 CCII 其MOS 電晶體之長寬比值 9
表2-3 OTRA內部MOS長寬比 26
表2-4 OTA與OTRA之對偶性 28
表4-1 各被動元件的理論值 52
表4-2 近似與非近似分析比較 55
表4-3 各OTRA輸入端電壓 57
表4-4 輸入端虛短路誤差分析 58
表4-5 變動L時的Vbias、amplitude與THD值 65

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